Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

Effect of 4 years of growth hormone therapy in children with Noonan syndrome in the American Norditropin Studies: Web-Enabled Research (ANSWER) Program® registry.

BACKGROUND: Noonan syndrome (NS) is a genetic disorder characterized by phenotypic features, including facial dysmorphology, cardiovascular anomalies, and short stature. Growth hormone (GH) has been approved by the United States Food and Drug Administration for short stature in children with NS. The objective of this analysis was to assess the height standard deviation score (HSDS) and change in HSDS (ΔHSDS) for up to 4 years (Y4) of GH therapy in children with NS. METHODS: The American Norditropin Studies: Web-Enabled Research (ANSWER) Program®, a US-based registry, collects long-term efficacy and safety information on patients treated with Norditropin® (somatropin rDNA origin, Novo Nordisk A/S) at the discretion of participating physicians. A total of 120 children (90 boys, 30 girls) with NS, naïve to previous GH treatment, were included in this analysis. RESULTS: The mean (SD) baseline age of subjects (n = 120) was 9.2 (3.8) years. Mean (SD) HSDS increased from -2.65 (0.73) at baseline to -1.32 (1.11) at Y4 (n = 17). Subjects showed continued increase in HSDS from baseline to Y4 without significant differences between genders at Y1 or Y2. The mean (SD) GH dose was 47 (11) mcg/kg/day at baseline and 59 (16) mcg/kg/day at Y4. There was a negative correlation between baseline age and ΔHSDS at Y1 (R = -0.3156; P = 0.0055) and Y2 (R = -0.3394; P = 0.017). ΔHSDS at Y1 was significantly correlated with ΔHSDS at Y2 (n = 37; R = 0.8527, P \u3c 0.0001) and Y3 (n = 20; R = 0.5145; P = 0.0203), but not Y4 (n = 12; R = 0.4066, P = 0.1896). CONCLUSIONS: GH treatment-naïve patients with NS showed continued increases in HSDS during 4 years of treatment with GH with no significant differences between genders up to 2 years. Baseline age was negatively correlated with ΔHSDS at Y1 and Y2. Whether long-term therapy in NS results in continued increase in HSDS to adult height remains to be investigated. TRIAL REGISTRATION: ClinicalTrials.gov NCT01009905

303. Image registration – precise quality assessment of radiotherapy without necessity of showing corresponding points in simulation and portal images

PurposeEnabling the quality assessment of radiotherapy to be made in daily practice, using the new software tool to analyze the simulation and portal images.MethodIn the registration of the anatomical structures as well as the irradiation fields, the features used as landmarks are the edges. The significant edge fragments must be chosen manually, but without showing any specific corresponding points. Field edges marked with wires in the simulation image are found fully automatically with the original combination of a dedicated line edge detector and a version of hierarchical, combined Hough transform. The registration is guided by the robust accuracy criterion using the modified Hausdorff distance measure. The only parameter of the measure – quantile rank, or share of data used in comparison – is not fixed, but evolves from 1 to 0 during the optimization of the accuracy. This has two advantages. 1: The user can choose the result found for the share corresponding to the actual share of erroneous data in the images, which can be seen only after the results for all the possible ranks are known. 2: The algorithm can avoid the local minima. The registration takes few seconds on a typical PC. The method has been implemented in a software tool which supports the complete process of measurement, and has been tested in clinical triais with positive result.ConclusionsThe modified Hausdorff distance measure with evolving rank is a good and efficient registration accuracy measure for quality assessment of radiotherapy based on the comparison of portal and simulation images

The problem of psychological rehabilitation of persons with disorders of the musculoskeletal system acquired in adulthood

The aim of this study was to study the psychological characteristics of persons with acquired disorders of the musculoskeletal system and to determine the direction and content of psychological rehabilitatio

Game-theoretic versions of strong law of large numbers for unbounded variables

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices

Factors Influencing the One- and Two-Year Growth Response in Children Treated with Growth Hormone: Analysis from an Observational Study

To assess gender-, pubertal-, age-related differences in change from baseline height standard deviation score (ΔHSDS), data from 5,797 growth hormone (GH) naïve pediatric patients (<18 years) with growth hormone deficiency (GHD), multiple pituitary hormone deficiency (MPHD), Turner syndrome (TS), small for gestational age (SGA), Noonan syndrome (NS), and idiopathic short stature (ISS) were obtained from the ANSWER (American Norditropin Studies: Web-enabled Research) Program registry. For patients with SGA, ΔHSDS at year 1 was significantly greater for males versus females (P = .016), but no other gender differences were observed. For patients with GHD, ΔHSDS was greater in prepubertal than in pubertal patients. Younger patients for both genders (<11 years for boys; <10 years for girls) showed a greater ΔHSDS (P < .05 for GHD, MPHD, and ISS). Overall, positive ΔHSDSs were observed in all patients, with greater growth responses in younger prepubertal children, emphasizing the importance of starting GH treatment early

3/Evaluation of set-up deviations during the irradiation of patients suffering from breast cancer treated with two different techniques

PurposeTo present results of patient positioning during routine radiotherapy for patients treated after mastectomy and to compare the inaccuracies in patient set-up for this group of patients and for the patients treated after breast conserving therapy with tangential fields.Methods and materialsIn total, the analysis comprised 56 pairs of portal and simulator films for 14 consecutive patients treated following breast conserving therapy and 98 pairs of portal and simulator films for 20 consecutive patients treated after mastectomy. For the first group the tangential field technique (TF technique) was used, for the second the inverse hockey stick technique (IHS technique). The comparison of the treatment reproducibility obtained for both groups of patients was performed in terms of systematic and random error calculated for the whole groups and by the comparison of cumulative distribution of the length of the displacement vector.ResultsIn the IHS and TF techniques for medial and lateral fields, displacement larger than 5 mm occurred in 28.3%, 15.8% and 25.4% respectively. For the IHS technique, the systematic errors for lateral and cranial-caudal direction were 1.9 and 1.7 mm respectively (1 standard deviation – SD), the random errors for lateral and cranial-caudal direction were 2.0 and 2.5 mm. For the TF technique, the systematic errors for lateral and cranial-caudal direction were 2.6 and 1.3 mm for medial field and 3.7 and 0.7 mm for lateral fields respectively, the random errors for lateral and cranial-caudal direction were 2.2 and 1.0 mm for medial field and 2.9 and 1.1 for lateral field respectively. Rotations were negligible in the HIS technique. For the TF technique the systematic component and random component amounted to about 2.0 degrees (1 SD).ConclusionsBoth the inverse hockey stick and standard tangential techniques showed good reproducibility of patients set-up with respect to cranial-caudal direction. For the TF technique, the accuracy should be improved for the medial field with respect to the ventral-dorsal direction